Nonperturbatively-renormalized glue momentum fraction at physical pion mass from Lattice QCD

TL;DR

This paper reports the first nonperturbative lattice QCD calculation of the gluon momentum fraction in the nucleon at physical pion mass, achieving high precision and consistency with experimental data.

Contribution

It introduces a practical nonperturbative renormalization strategy for the gluon energy-momentum tensor in lattice QCD and applies it to determine the gluon momentum fraction.

Findings

Renormalized gluon momentum fraction is 0.47(4)(11) at 2 GeV.

CDER technique reduces renormalization uncertainty by a factor of about 300.

Results are consistent across different lattice definitions of the glue EMT.

Abstract

We present the first nonperturbatively-renormalized determination of the glue momentum fraction $\langle x \rangle_g$ in the nucleon, based on lattice-QCD simulations at physical pion mass using the cluster-decomposition error reduction (CDER) technique. We provide the first practical strategy to renormalize the glue energy-momentum tensor (EMT) nonperturbatively in the RI/MOM scheme, and convert the results to the $\overline{\textrm{MS}}$ scheme with 1-loop matching. The simulation results show that the CDER technique can reduce the statistical uncertainty of its renormalization constant by a factor of ${\cal O}$(300) in calculations using typical state-of-the-art lattice volume, and the nonperturbatively-renormalized $\langle x \rangle_g$ is shown to be independent of the lattice definitions of the glue EMT up to discretization errors. We determine the renormalized $\langle x \rangle_g^{\overline{\textrm{MS}}}(2\textrm{ GeV})$ to be 0.47(4)(11) at physical pion mass, which is consistent with the experimentally-determined value.